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#1
11-18-2008, 12:47 PM
 vvkannan Senior Member Join Date: Aug 2008 Location: India Posts: 137
Boolean function implementation

I have some doubts regarding boolean function implementation using multiplexers.
If i have to implement a product of sum function like this
example:F(A,B,C,D)=pi M(0,3,5,7,8,9)+d(2,6)
and i convert this POS into SOP expression.should i have to remove all the dont cares?
Taking the above example should i write :sum m( 1,,4,10..15) or should i include the dont cares?
Cant we implement a boolean function directly from a POS expression?
Thank you
#2
11-18-2008, 04:52 PM
 Ratch Banned Join Date: Mar 2007 Posts: 1,068

vvkannan,

Quote:
 I have some doubts regarding boolean function implementation using multiplexers
I will try to eradicate those doubts. By the way, Boolean is capitalized because it is derived from a person's name. So is the personal pronoun "I" capitalized. And contractions use an apostrophe.

Quote:
 If i have to implement a product of sum function like this example:F(A,B,C,D)=pi M(0,3,5,7,8,9)+d(2,6) and i convert this POS into SOP expression.should i have to remove all the dont cares? Taking the above example should i write :sum m( 1,,4,10..15) or should i include the dont cares?
You include the don't cares because their terms can be present or missing in either the SOP or POS form of the equation.

Quote:
 Cant we implement a boolean function directly from a POS expression?
Certainly, just use a AND gate instead of an OR gate.

Ratch
#3
11-19-2008, 12:04 PM
 vvkannan Senior Member Join Date: Aug 2008 Location: India Posts: 137

Thank you for correcting me.

So don't cares can either be included or not and it would not make any difference .
Thank you
#4
11-19-2008, 02:55 PM
 Ratch Banned Join Date: Mar 2007 Posts: 1,068

vvkannan,

Quote:
 So don't cares can either be included or not and it would not make any difference .
Oh, oh, I think you misunderstood me. I said that the terms that the don't cares represent could either be present or missing. Let me clarify. You use the don't cares if you need them to simplify a expression and discard them if you don't. It does make a difference if you don't use them if they can simplify a expression. In your example, PI M(0,3,5,7,8,9)+d(2,6), the complement is either SIGMA m(1,2,4,6,10-15) or SIGMA m(1,2,4,10-15) . The only difference between the two SIGMA expressions is the presence or absence of SIGMA m(2,6) . That is the definition of don't cares, so you can write the complement of PI M(0,3,5,7,8,9)+d(2,6) as SIGMA m(1,2,4,10-15)+d(2,6) . Another way to understand it better is to make a truth table and mark the don't cares with a "X". Then you can see that the don't care terms can be used for either the original expression or its complement.

Ratch
#5
11-20-2008, 03:18 PM
 vvkannan Senior Member Join Date: Aug 2008 Location: India Posts: 137

Thank you very much .Now you really have eradicated my doubts.

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